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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.analysis.interpolation;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import java.util.ArrayList;<a name="line.19"></a>
<FONT color="green">020</FONT>    import java.util.HashMap;<a name="line.20"></a>
<FONT color="green">021</FONT>    import java.util.List;<a name="line.21"></a>
<FONT color="green">022</FONT>    import java.util.Map;<a name="line.22"></a>
<FONT color="green">023</FONT>    <a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.analysis.MultivariateFunction;<a name="line.24"></a>
<FONT color="green">025</FONT>    import org.apache.commons.math3.exception.DimensionMismatchException;<a name="line.25"></a>
<FONT color="green">026</FONT>    import org.apache.commons.math3.exception.NoDataException;<a name="line.26"></a>
<FONT color="green">027</FONT>    import org.apache.commons.math3.exception.NullArgumentException;<a name="line.27"></a>
<FONT color="green">028</FONT>    import org.apache.commons.math3.linear.ArrayRealVector;<a name="line.28"></a>
<FONT color="green">029</FONT>    import org.apache.commons.math3.linear.RealVector;<a name="line.29"></a>
<FONT color="green">030</FONT>    import org.apache.commons.math3.random.UnitSphereRandomVectorGenerator;<a name="line.30"></a>
<FONT color="green">031</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.31"></a>
<FONT color="green">032</FONT>    <a name="line.32"></a>
<FONT color="green">033</FONT>    /**<a name="line.33"></a>
<FONT color="green">034</FONT>     * Interpolating function that implements the<a name="line.34"></a>
<FONT color="green">035</FONT>     * &lt;a href="http://www.dudziak.com/microsphere.php"&gt;Microsphere Projection&lt;/a&gt;.<a name="line.35"></a>
<FONT color="green">036</FONT>     *<a name="line.36"></a>
<FONT color="green">037</FONT>     * @version $Id: MicrosphereInterpolatingFunction.java 1379904 2012-09-01 23:54:52Z erans $<a name="line.37"></a>
<FONT color="green">038</FONT>     */<a name="line.38"></a>
<FONT color="green">039</FONT>    public class MicrosphereInterpolatingFunction<a name="line.39"></a>
<FONT color="green">040</FONT>        implements MultivariateFunction {<a name="line.40"></a>
<FONT color="green">041</FONT>        /**<a name="line.41"></a>
<FONT color="green">042</FONT>         * Space dimension.<a name="line.42"></a>
<FONT color="green">043</FONT>         */<a name="line.43"></a>
<FONT color="green">044</FONT>        private final int dimension;<a name="line.44"></a>
<FONT color="green">045</FONT>        /**<a name="line.45"></a>
<FONT color="green">046</FONT>         * Internal accounting data for the interpolation algorithm.<a name="line.46"></a>
<FONT color="green">047</FONT>         * Each element of the list corresponds to one surface element of<a name="line.47"></a>
<FONT color="green">048</FONT>         * the microsphere.<a name="line.48"></a>
<FONT color="green">049</FONT>         */<a name="line.49"></a>
<FONT color="green">050</FONT>        private final List&lt;MicrosphereSurfaceElement&gt; microsphere;<a name="line.50"></a>
<FONT color="green">051</FONT>        /**<a name="line.51"></a>
<FONT color="green">052</FONT>         * Exponent used in the power law that computes the weights of the<a name="line.52"></a>
<FONT color="green">053</FONT>         * sample data.<a name="line.53"></a>
<FONT color="green">054</FONT>         */<a name="line.54"></a>
<FONT color="green">055</FONT>        private final double brightnessExponent;<a name="line.55"></a>
<FONT color="green">056</FONT>        /**<a name="line.56"></a>
<FONT color="green">057</FONT>         * Sample data.<a name="line.57"></a>
<FONT color="green">058</FONT>         */<a name="line.58"></a>
<FONT color="green">059</FONT>        private final Map&lt;RealVector, Double&gt; samples;<a name="line.59"></a>
<FONT color="green">060</FONT>    <a name="line.60"></a>
<FONT color="green">061</FONT>        /**<a name="line.61"></a>
<FONT color="green">062</FONT>         * Class for storing the accounting data needed to perform the<a name="line.62"></a>
<FONT color="green">063</FONT>         * microsphere projection.<a name="line.63"></a>
<FONT color="green">064</FONT>         */<a name="line.64"></a>
<FONT color="green">065</FONT>        private static class MicrosphereSurfaceElement {<a name="line.65"></a>
<FONT color="green">066</FONT>            /** Normal vector characterizing a surface element. */<a name="line.66"></a>
<FONT color="green">067</FONT>            private final RealVector normal;<a name="line.67"></a>
<FONT color="green">068</FONT>            /** Illumination received from the brightest sample. */<a name="line.68"></a>
<FONT color="green">069</FONT>            private double brightestIllumination;<a name="line.69"></a>
<FONT color="green">070</FONT>            /** Brightest sample. */<a name="line.70"></a>
<FONT color="green">071</FONT>            private Map.Entry&lt;RealVector, Double&gt; brightestSample;<a name="line.71"></a>
<FONT color="green">072</FONT>    <a name="line.72"></a>
<FONT color="green">073</FONT>            /**<a name="line.73"></a>
<FONT color="green">074</FONT>             * @param n Normal vector characterizing a surface element<a name="line.74"></a>
<FONT color="green">075</FONT>             * of the microsphere.<a name="line.75"></a>
<FONT color="green">076</FONT>             */<a name="line.76"></a>
<FONT color="green">077</FONT>            MicrosphereSurfaceElement(double[] n) {<a name="line.77"></a>
<FONT color="green">078</FONT>                normal = new ArrayRealVector(n);<a name="line.78"></a>
<FONT color="green">079</FONT>            }<a name="line.79"></a>
<FONT color="green">080</FONT>    <a name="line.80"></a>
<FONT color="green">081</FONT>            /**<a name="line.81"></a>
<FONT color="green">082</FONT>             * Return the normal vector.<a name="line.82"></a>
<FONT color="green">083</FONT>             * @return the normal vector<a name="line.83"></a>
<FONT color="green">084</FONT>             */<a name="line.84"></a>
<FONT color="green">085</FONT>            RealVector normal() {<a name="line.85"></a>
<FONT color="green">086</FONT>                return normal;<a name="line.86"></a>
<FONT color="green">087</FONT>            }<a name="line.87"></a>
<FONT color="green">088</FONT>    <a name="line.88"></a>
<FONT color="green">089</FONT>            /**<a name="line.89"></a>
<FONT color="green">090</FONT>             * Reset "illumination" and "sampleIndex".<a name="line.90"></a>
<FONT color="green">091</FONT>             */<a name="line.91"></a>
<FONT color="green">092</FONT>            void reset() {<a name="line.92"></a>
<FONT color="green">093</FONT>                brightestIllumination = 0;<a name="line.93"></a>
<FONT color="green">094</FONT>                brightestSample = null;<a name="line.94"></a>
<FONT color="green">095</FONT>            }<a name="line.95"></a>
<FONT color="green">096</FONT>    <a name="line.96"></a>
<FONT color="green">097</FONT>            /**<a name="line.97"></a>
<FONT color="green">098</FONT>             * Store the illumination and index of the brightest sample.<a name="line.98"></a>
<FONT color="green">099</FONT>             * @param illuminationFromSample illumination received from sample<a name="line.99"></a>
<FONT color="green">100</FONT>             * @param sample current sample illuminating the element<a name="line.100"></a>
<FONT color="green">101</FONT>             */<a name="line.101"></a>
<FONT color="green">102</FONT>            void store(final double illuminationFromSample,<a name="line.102"></a>
<FONT color="green">103</FONT>                       final Map.Entry&lt;RealVector, Double&gt; sample) {<a name="line.103"></a>
<FONT color="green">104</FONT>                if (illuminationFromSample &gt; this.brightestIllumination) {<a name="line.104"></a>
<FONT color="green">105</FONT>                    this.brightestIllumination = illuminationFromSample;<a name="line.105"></a>
<FONT color="green">106</FONT>                    this.brightestSample = sample;<a name="line.106"></a>
<FONT color="green">107</FONT>                }<a name="line.107"></a>
<FONT color="green">108</FONT>            }<a name="line.108"></a>
<FONT color="green">109</FONT>    <a name="line.109"></a>
<FONT color="green">110</FONT>            /**<a name="line.110"></a>
<FONT color="green">111</FONT>             * Get the illumination of the element.<a name="line.111"></a>
<FONT color="green">112</FONT>             * @return the illumination.<a name="line.112"></a>
<FONT color="green">113</FONT>             */<a name="line.113"></a>
<FONT color="green">114</FONT>            double illumination() {<a name="line.114"></a>
<FONT color="green">115</FONT>                return brightestIllumination;<a name="line.115"></a>
<FONT color="green">116</FONT>            }<a name="line.116"></a>
<FONT color="green">117</FONT>    <a name="line.117"></a>
<FONT color="green">118</FONT>            /**<a name="line.118"></a>
<FONT color="green">119</FONT>             * Get the sample illuminating the element the most.<a name="line.119"></a>
<FONT color="green">120</FONT>             * @return the sample.<a name="line.120"></a>
<FONT color="green">121</FONT>             */<a name="line.121"></a>
<FONT color="green">122</FONT>            Map.Entry&lt;RealVector, Double&gt; sample() {<a name="line.122"></a>
<FONT color="green">123</FONT>                return brightestSample;<a name="line.123"></a>
<FONT color="green">124</FONT>            }<a name="line.124"></a>
<FONT color="green">125</FONT>        }<a name="line.125"></a>
<FONT color="green">126</FONT>    <a name="line.126"></a>
<FONT color="green">127</FONT>        /**<a name="line.127"></a>
<FONT color="green">128</FONT>         * @param xval Arguments for the interpolation points.<a name="line.128"></a>
<FONT color="green">129</FONT>         * {@code xval[i][0]} is the first component of interpolation point<a name="line.129"></a>
<FONT color="green">130</FONT>         * {@code i}, {@code xval[i][1]} is the second component, and so on<a name="line.130"></a>
<FONT color="green">131</FONT>         * until {@code xval[i][d-1]}, the last component of that interpolation<a name="line.131"></a>
<FONT color="green">132</FONT>         * point (where {@code dimension} is thus the dimension of the sampled<a name="line.132"></a>
<FONT color="green">133</FONT>         * space).<a name="line.133"></a>
<FONT color="green">134</FONT>         * @param yval Values for the interpolation points.<a name="line.134"></a>
<FONT color="green">135</FONT>         * @param brightnessExponent Brightness dimming factor.<a name="line.135"></a>
<FONT color="green">136</FONT>         * @param microsphereElements Number of surface elements of the<a name="line.136"></a>
<FONT color="green">137</FONT>         * microsphere.<a name="line.137"></a>
<FONT color="green">138</FONT>         * @param rand Unit vector generator for creating the microsphere.<a name="line.138"></a>
<FONT color="green">139</FONT>         * @throws DimensionMismatchException if the lengths of {@code yval} and<a name="line.139"></a>
<FONT color="green">140</FONT>         * {@code xval} (equal to {@code n}, the number of interpolation points)<a name="line.140"></a>
<FONT color="green">141</FONT>         * do not match, or the the arrays {@code xval[0]} ... {@code xval[n]},<a name="line.141"></a>
<FONT color="green">142</FONT>         * have lengths different from {@code dimension}.<a name="line.142"></a>
<FONT color="green">143</FONT>         * @throws NoDataException if there an array has zero-length.<a name="line.143"></a>
<FONT color="green">144</FONT>         * @throws NullArgumentException if an argument is {@code null}.<a name="line.144"></a>
<FONT color="green">145</FONT>         */<a name="line.145"></a>
<FONT color="green">146</FONT>        public MicrosphereInterpolatingFunction(double[][] xval,<a name="line.146"></a>
<FONT color="green">147</FONT>                                                double[] yval,<a name="line.147"></a>
<FONT color="green">148</FONT>                                                int brightnessExponent,<a name="line.148"></a>
<FONT color="green">149</FONT>                                                int microsphereElements,<a name="line.149"></a>
<FONT color="green">150</FONT>                                                UnitSphereRandomVectorGenerator rand)<a name="line.150"></a>
<FONT color="green">151</FONT>            throws DimensionMismatchException,<a name="line.151"></a>
<FONT color="green">152</FONT>                   NoDataException,<a name="line.152"></a>
<FONT color="green">153</FONT>                   NullArgumentException {<a name="line.153"></a>
<FONT color="green">154</FONT>            if (xval == null ||<a name="line.154"></a>
<FONT color="green">155</FONT>                yval == null) {<a name="line.155"></a>
<FONT color="green">156</FONT>                throw new NullArgumentException();<a name="line.156"></a>
<FONT color="green">157</FONT>            }<a name="line.157"></a>
<FONT color="green">158</FONT>            if (xval.length == 0) {<a name="line.158"></a>
<FONT color="green">159</FONT>                throw new NoDataException();<a name="line.159"></a>
<FONT color="green">160</FONT>            }<a name="line.160"></a>
<FONT color="green">161</FONT>            if (xval.length != yval.length) {<a name="line.161"></a>
<FONT color="green">162</FONT>                throw new DimensionMismatchException(xval.length, yval.length);<a name="line.162"></a>
<FONT color="green">163</FONT>            }<a name="line.163"></a>
<FONT color="green">164</FONT>            if (xval[0] == null) {<a name="line.164"></a>
<FONT color="green">165</FONT>                throw new NullArgumentException();<a name="line.165"></a>
<FONT color="green">166</FONT>            }<a name="line.166"></a>
<FONT color="green">167</FONT>    <a name="line.167"></a>
<FONT color="green">168</FONT>            dimension = xval[0].length;<a name="line.168"></a>
<FONT color="green">169</FONT>            this.brightnessExponent = brightnessExponent;<a name="line.169"></a>
<FONT color="green">170</FONT>    <a name="line.170"></a>
<FONT color="green">171</FONT>            // Copy data samples.<a name="line.171"></a>
<FONT color="green">172</FONT>            samples = new HashMap&lt;RealVector, Double&gt;(yval.length);<a name="line.172"></a>
<FONT color="green">173</FONT>            for (int i = 0; i &lt; xval.length; ++i) {<a name="line.173"></a>
<FONT color="green">174</FONT>                final double[] xvalI = xval[i];<a name="line.174"></a>
<FONT color="green">175</FONT>                if (xvalI == null) {<a name="line.175"></a>
<FONT color="green">176</FONT>                    throw new NullArgumentException();<a name="line.176"></a>
<FONT color="green">177</FONT>                }<a name="line.177"></a>
<FONT color="green">178</FONT>                if (xvalI.length != dimension) {<a name="line.178"></a>
<FONT color="green">179</FONT>                    throw new DimensionMismatchException(xvalI.length, dimension);<a name="line.179"></a>
<FONT color="green">180</FONT>                }<a name="line.180"></a>
<FONT color="green">181</FONT>    <a name="line.181"></a>
<FONT color="green">182</FONT>                samples.put(new ArrayRealVector(xvalI), yval[i]);<a name="line.182"></a>
<FONT color="green">183</FONT>            }<a name="line.183"></a>
<FONT color="green">184</FONT>    <a name="line.184"></a>
<FONT color="green">185</FONT>            microsphere = new ArrayList&lt;MicrosphereSurfaceElement&gt;(microsphereElements);<a name="line.185"></a>
<FONT color="green">186</FONT>            // Generate the microsphere, assuming that a fairly large number of<a name="line.186"></a>
<FONT color="green">187</FONT>            // randomly generated normals will represent a sphere.<a name="line.187"></a>
<FONT color="green">188</FONT>            for (int i = 0; i &lt; microsphereElements; i++) {<a name="line.188"></a>
<FONT color="green">189</FONT>                microsphere.add(new MicrosphereSurfaceElement(rand.nextVector()));<a name="line.189"></a>
<FONT color="green">190</FONT>            }<a name="line.190"></a>
<FONT color="green">191</FONT>        }<a name="line.191"></a>
<FONT color="green">192</FONT>    <a name="line.192"></a>
<FONT color="green">193</FONT>        /**<a name="line.193"></a>
<FONT color="green">194</FONT>         * @param point Interpolation point.<a name="line.194"></a>
<FONT color="green">195</FONT>         * @return the interpolated value.<a name="line.195"></a>
<FONT color="green">196</FONT>         */<a name="line.196"></a>
<FONT color="green">197</FONT>        public double value(double[] point) {<a name="line.197"></a>
<FONT color="green">198</FONT>            final RealVector p = new ArrayRealVector(point);<a name="line.198"></a>
<FONT color="green">199</FONT>    <a name="line.199"></a>
<FONT color="green">200</FONT>            // Reset.<a name="line.200"></a>
<FONT color="green">201</FONT>            for (MicrosphereSurfaceElement md : microsphere) {<a name="line.201"></a>
<FONT color="green">202</FONT>                md.reset();<a name="line.202"></a>
<FONT color="green">203</FONT>            }<a name="line.203"></a>
<FONT color="green">204</FONT>    <a name="line.204"></a>
<FONT color="green">205</FONT>            // Compute contribution of each sample points to the microsphere elements illumination<a name="line.205"></a>
<FONT color="green">206</FONT>            for (Map.Entry&lt;RealVector, Double&gt; sd : samples.entrySet()) {<a name="line.206"></a>
<FONT color="green">207</FONT>    <a name="line.207"></a>
<FONT color="green">208</FONT>                // Vector between interpolation point and current sample point.<a name="line.208"></a>
<FONT color="green">209</FONT>                final RealVector diff = sd.getKey().subtract(p);<a name="line.209"></a>
<FONT color="green">210</FONT>                final double diffNorm = diff.getNorm();<a name="line.210"></a>
<FONT color="green">211</FONT>    <a name="line.211"></a>
<FONT color="green">212</FONT>                if (FastMath.abs(diffNorm) &lt; FastMath.ulp(1d)) {<a name="line.212"></a>
<FONT color="green">213</FONT>                    // No need to interpolate, as the interpolation point is<a name="line.213"></a>
<FONT color="green">214</FONT>                    // actually (very close to) one of the sampled points.<a name="line.214"></a>
<FONT color="green">215</FONT>                    return sd.getValue();<a name="line.215"></a>
<FONT color="green">216</FONT>                }<a name="line.216"></a>
<FONT color="green">217</FONT>    <a name="line.217"></a>
<FONT color="green">218</FONT>                for (MicrosphereSurfaceElement md : microsphere) {<a name="line.218"></a>
<FONT color="green">219</FONT>                    final double w = FastMath.pow(diffNorm, -brightnessExponent);<a name="line.219"></a>
<FONT color="green">220</FONT>                    md.store(cosAngle(diff, md.normal()) * w, sd);<a name="line.220"></a>
<FONT color="green">221</FONT>                }<a name="line.221"></a>
<FONT color="green">222</FONT>    <a name="line.222"></a>
<FONT color="green">223</FONT>            }<a name="line.223"></a>
<FONT color="green">224</FONT>    <a name="line.224"></a>
<FONT color="green">225</FONT>            // Interpolation calculation.<a name="line.225"></a>
<FONT color="green">226</FONT>            double value = 0;<a name="line.226"></a>
<FONT color="green">227</FONT>            double totalWeight = 0;<a name="line.227"></a>
<FONT color="green">228</FONT>            for (MicrosphereSurfaceElement md : microsphere) {<a name="line.228"></a>
<FONT color="green">229</FONT>                final double iV = md.illumination();<a name="line.229"></a>
<FONT color="green">230</FONT>                final Map.Entry&lt;RealVector, Double&gt; sd = md.sample();<a name="line.230"></a>
<FONT color="green">231</FONT>                if (sd != null) {<a name="line.231"></a>
<FONT color="green">232</FONT>                    value += iV * sd.getValue();<a name="line.232"></a>
<FONT color="green">233</FONT>                    totalWeight += iV;<a name="line.233"></a>
<FONT color="green">234</FONT>                }<a name="line.234"></a>
<FONT color="green">235</FONT>            }<a name="line.235"></a>
<FONT color="green">236</FONT>    <a name="line.236"></a>
<FONT color="green">237</FONT>            return value / totalWeight;<a name="line.237"></a>
<FONT color="green">238</FONT>        }<a name="line.238"></a>
<FONT color="green">239</FONT>    <a name="line.239"></a>
<FONT color="green">240</FONT>        /**<a name="line.240"></a>
<FONT color="green">241</FONT>         * Compute the cosine of the angle between 2 vectors.<a name="line.241"></a>
<FONT color="green">242</FONT>         *<a name="line.242"></a>
<FONT color="green">243</FONT>         * @param v Vector.<a name="line.243"></a>
<FONT color="green">244</FONT>         * @param w Vector.<a name="line.244"></a>
<FONT color="green">245</FONT>         * @return the cosine of the angle between {@code v} and {@code w}.<a name="line.245"></a>
<FONT color="green">246</FONT>         */<a name="line.246"></a>
<FONT color="green">247</FONT>        private double cosAngle(final RealVector v, final RealVector w) {<a name="line.247"></a>
<FONT color="green">248</FONT>            return v.dotProduct(w) / (v.getNorm() * w.getNorm());<a name="line.248"></a>
<FONT color="green">249</FONT>        }<a name="line.249"></a>
<FONT color="green">250</FONT>    }<a name="line.250"></a>




























































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